This is exactly what ds did - for about the first two weeks. In hindsight, probably because my boobs were enormous and he was tiny (and probably suffering one hell of a headache after forceps!) I realise now that it was a bit like asking him to suck the air out of a spacehopper! So, considering how little milk they actually take at this point, maybe it is worth expressing a bit more to make sure milk comes out easily? That said, maybe the milk is coming out too quickly and that is what is distressing your dd? (Sorry, not being much help, am I?)
Also - and don't want to get too personal - but if you have quite flat nipples make sure you pump first to help "bring them out of themselves". I had this problem and used nipple shields for a week as it seemed to help ds get a grip! Then, once he started to get the hang of things, I dumped them.
Also have you eaten anything in the last day that could make your milk taste different (curry/Thai for instance?) Might be a cause for complaint . Also, I have been told that around day 4 - 6 around is when your hormones wear off and the babies kick in, and that it invariably causes the day (and night) from hell.
Would definitely also play around with positions also. Remember many babies don't get breastfeeding straight away - the important thing is to try not to get too stressed. It took ds blooming ages and I was at the point of giving up when he finally got the knack. Ended up bf for a year - probably why ds regularly tells me how much he "loves my boobies" - he's 4. Very sweet - except when we are in public.